A Practical Study On The Combination Of Numbers And Shapes In The Teaching Of Mathematics In Upper Primary Schools

With the development of society and the renewal of education,the important role of mathematical ideas is increasingly emphasized in modern primary school mathematics teaching,and the idea of combining numbers and shapes is one of the very important mathematical ideas.The application of the idea of combining numbers and shapes in mathematics learning can not only help students vividly understand abstract quantitative relationships such as mathematical formulas and mathematical symbols through intuitive "shapes",but also describe and analyze graphics through accurate "numbers" to help them better grasp the characteristics and properties of graphics.Therefore,the combination of numbers and shapes is not only conducive to students’ understanding and grasp of the essence of mathematical knowledge,but also can lay an ideological foundation for their future mathematical learning.However,during the internship in a primary school in Jinan City,the author found that many teachers still have many problems when infiltrating the idea of combining numbers and shapes into students,so this study is based on the teaching practice of the idea of combining numbers and shapes in the upper grades of primary school,using literature analysis method,questionnaire survey method and interview method,to analyze the problems and reasons of teachers’ application of the idea of combining numbers and shapes in teaching,and propose corresponding solutions for teachers accordingly.This study is divided into five parts:The first part is an introduction,which clarifies the background,theoretical significance and practical significance of the research,and expounds the connotation,teaching role,teaching status and teaching strategy of domestic and foreign scholars on the combination of numbers and shapes through literature analysis,and defines the core concepts of this paper,and finally explains the research ideas of this paper,and introduces in detail the research methods of this paper and the implementation process of teacher questionnaires and teacher interviews.The second part is the theoretical elaboration of the implementation of the idea of combining numbers and shapes,including cognitive representation theory,constructivist theory and Piaget’s theory of stages of cognitive development,and elaborates the connotation characteristics of these three theories and their relevance in the teaching of combination of numbers and shapes.The third part,by analyzing the results of the teacher questionnaire and the specific content of the teacher interview,it is found that when the teachers of upper primary school apply the idea of combining numbers and shapes in teaching,they do not have a deep understanding of the connotation of the idea of combining numbers and shapes,the idea of combining numbers and shapes is not fully reflected in the teaching design,and the application of the idea of combining numbers and shapes is not in-depth in the teaching process.The fourth part starts from the three aspects of pre-service education,schools and teachers themselves,and analyzes the reasons for the problems existing in the application of the idea of combining numbers and shapes in the teaching of upper primary schools,one is due to the lack of guidance in pre-service education to guide teachers to systematically learn the idea of combining numbers and shapes,the second is due to the lack of guidance and support for teachers to combine numbers and shapes,and the third is due to the lack of in-depth research on the teaching of number and shape combination by teachers themselves.The last part puts forward the strategic choices for teachers in the upper primary school to implement the teaching of the combination of numbers and shapes,firstly,to improve the teaching literacy of teachers who combine the ideas of numbers and shapes;The second is to deeply explore the combination of numbers and shapes contained in the textbooks;The third is to strengthen the exploration of the idea of infiltrating the combination of numbers and shapes in different knowledge fields;The fourth is to optimize the teaching process of combining numbers and shapes with ideological practice.